Potential difference Capacitance problem

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Homework Help Overview

The discussion revolves around a capacitor arrangement where a potential difference of 100 V is applied. The problem involves capacitors C1, C2, and C3 with values of 10 microF, 5 microF, and 4 microF respectively, and explores the effects of electrical breakdown in C3 on the charge and potential difference across C1.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to find the equivalent capacitance and total charge, leading to calculations of individual charges and potential differences. They express uncertainty about their reasoning and seek clarification on their assumptions regarding charge relationships.

Discussion Status

Participants are actively questioning the assumptions made about the relationships between the charges on the capacitors. There is a recognition of a mistake in the original poster's reasoning regarding the total charge and its distribution among the capacitors. Multiple interpretations of the charge relationships are being explored.

Contextual Notes

There is an indication of confusion regarding the application of charge conservation principles in the context of series and parallel capacitor configurations. The original poster also notes a discrepancy in their calculations compared to expected results.

endeavor
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Homework Statement


http://img509.imageshack.us/img509/8805/problem5fw8.th.png
The potential difference V = 100 V is applied to the capacitor arrangement shown in the figure. Here C1 = 10 microF, C2 = 5 microF, and C3 = 4microF. If capacitor C3 undergoes electrical breakdown (i.e. becomes equivalent to a conducting wire), what is the increase in (a) the charge on capacitor 1, and (b) the potential difference across capacitor 1?

The Attempt at a Solution


I wasn't sure how to solve it so I started doing different things:
I first found the equivalent capacitance, and with that I found the total charge to be Q_tot = 3.16 * 10^-4 C.
Then, I thought since the equivalent of C1 and C2, and C3 are in series, Q1 + Q2 = Q3, so Q_tot = 2 * Q3.
Then, from Q3 and C3, I find the potential difference across of C3 to be V3 = 39.5V, which in turn makes V1 = V2 = 60.5V.
From V1 and V2, I found the initial charges Q1 = 605 microC, and Q2 = 302.5 microC.
I'm not sure where to go from here...

I tried also to find the final potential difference across C1:
C12 = C1 + C2 = Q_tot / V_new
V_new = 21V, but it's supposed to be 79V... what am I doing wrong here?

Since Q = CV, if I plug in V = 79V, then Q1 = 790 microC, which is the answer for part (a), right? So should I try to solve part (b) first?

Any help would be greatly appreciated!

P.S. sorry for not using tex...
 
Last edited by a moderator:
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you've made a mistake

Q1 + Q2 = Q3, so Q_tot = 2 * Q3.

this is the faulty assumption

it should be
Q1 + Q2 = Q3 = Q_tot
 
But if Q1 + Q2 = Q3, and Q_tot = Q1 + Q2 + Q3, then Q_tot = Q3 + Q3 = 2*Q3 ... right?
 
endeavor said:
But if Q1 + Q2 = Q3, and Q_tot = Q1 + Q2 + Q3, then Q_tot = Q3 + Q3 = 2*Q3 ... right?

you just restated what i already said was wrong

Q_tot = Q1 + Q2 = Q3
 

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